Efficient methods in optimization



The lecture takes place on Tuesdays from 15:30 to 18:30 in room H101 (except on December 13: room H102).

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Script

Lecture 1: Introduction: modeling / formalization, problem classes, examples

Matlab implementations: uniform approximation, resource allocation, maximum flow

Lectures 2,3: Simple problems and methods, basic mathematics (convexity, affine spaces, separation, duality, faces, cones)

Matlab implementations: solution of LPs with the ellipsoid method

Lecture 4: Convexity

Lecture 5: Proximal and bundle methods

Lecture 6: Splitting methods

Lecture 7-8: Linear programming, slides

Lecture 8-9: Conic programming

Addendum: Applications of SDP

Lecture 10: Interior-point methods

Addendum: Robust conic programs

Lecture 11: Semi-definite relaxations, matlab programs Max Cut standard relaxation

Lecture 12: Polynomial optimization



References

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Examination


There will be a 2h written exam presumably in January. The last lecture will be dedicated to training for the exam.

Some examples of problems and some other examples.

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